Yes, your library should allow the process to exit without warning. Perhaps in an ideal world every program using your library would carefully track the handles and free them all when it exits for any reason, but in practice this isn't a realistic requirement. The code path that is triggering the program exit might be a shared component that isn't even aware that your library is in use!
In any case, it is likely that your current architecture has a more general problem, because it is inherently unsafe for static destructors to interact with other threads.
From DllMain entry point in MSDN:
Because DLL notifications are serialized, entry-point functions should not attempt to communicate with other threads or processes. Deadlocks may occur as a result.
and
If your DLL is linked with the C run-time library (CRT), the entry point provided by the CRT calls the constructors and destructors for global and static C++ objects. Therefore, these restrictions for DllMain also apply to constructors and destructors and any code that is called from them.
In particular, if your destructors attempt to wait for your threads to exit, that is almost certain to deadlock in the case where the library is explicitly unloaded while the threads are still running. If the destructors don't wait, the process will crash when the code the threads are running disappears. I'm not sure why you aren't seeing that problem already; perhaps you are terminating the threads? (That's not safe either, although for different reasons.)
There are a number of ways to resolve this problem. Probably the simplest is the one you already mentioned:
One possibility is to not have any global objects with destructors, and so to avoid running any code in the library during static destruction.
You go on to say:
[...] but it would introduce leaks and crashes in the scenario where the application simply unloads the library without freeing the handles [...]
That's not your problem! The library will only be unloaded if the application explicitly chooses to do so; obviously, and unlike the earlier scenario, the code in question knows your library is present, so it is perfectly reasonable for you to require that it close all your handles before doing so.
Ideally, however, you would provide an uninitialization function that closes all the handles automatically, rather than requiring the application to close each handle individually. Explicit initialization and uninitialization functions also allows you to safely set up and free global resources, which is usually more efficient than doing all of your setup and teardown on a per-handle basis and is certainly safer than using global objects.
(See the link above for a full description of all the restrictions applicable to static constructors and destructors; they are quite extensive. Constructing all your globals in an explicit initialization routine, and destroying them in an explicit uninitialization routine, avoids the whole messy business.)